Index > Course > 2021-03-09: Linear Programming
The test is a week from Thursday (March 18th). 4 hours are allocated (10AM to 2PM) - Prof. recommends allocating a 2 hour block inside that range.
Find some experts to elicit.
It’s like, maximizing a linear function.
Decision Variables: Inputs
Constraints:
Objective: One variable, that is a function of the inputs
I can make two types of hot tubs. One makes me 350 dollars, the other only 300
\[350X_1 + 300X_2\]I only have 200 pumps, and each model takes one.
\[1X_1 + 1X_2 \leq 200\]Each model takes time to build, and I have limited labor:
\[9X_1 + 6X_2 \leq 1566\]And there’s another constraint, on Tubing:
\[12X_1 + 16X_2 \leq 2880\](And of course, I can’t make negative hot tubs.)
Now, I technically could use tikzjax - but there’s not enough time in the week to figure it out. tikz is hard. So we’ll have to do with descriptions instead of real graphs.
On a 2D graph, with $X_1$ on one axis and $X_2$ on the other, we can graph the constraints as inequalities. The region bounded by the inequalities represents all possible solutions. The solution that maximizes your objective will be on one of the vertices.